Enter the x and y components of the velocity into the calculator to determine the magnitude and angle of the velocity.

Magnitude of Velocity Formula

The following equation is used to calculate the Magnitude of Velocity.

Vm = SQRT( Vx^2 + Vy^2)
a = atan (Vy/Vx)
  • Where Vm is the velocity magnitude (m/s)
  • Vx is the x-component of velocity (m/s)
  • Vy is the y-component of velocity (m/s)
  • a is the angle of the velocity (degrees)

To calculate the magnitude of a velocity vector, square both the x and y-components of velocity, add the result together, then finally take the square root of that value.

What is the Magnitude of Velocity?


A magnitude of velocity measures the hypotenuse between the x and y components of velocity.

How to Calculate Magnitude of Velocity?

Example Problem:

The following example outlines the steps and information needed to calculate Magnitude of Velocity.

First, determine the x-component of velocity. In this example, the x-component of velocity is found to be 30 m/s.

Next, determine the y-component of velocity. For this problem, the y-component of velocity is found to be 50 m/s.

Finally, calculate the Magnitude of Velocity using the formula above:

Vm = SQRT( Vx^2 + Vy^2)

Vm = SQRT( 30^2 + 50^2)

Vm = 58.309 m/s